### Abstract

The Do-All problem is about scheduling t similar and independent tasks to be performed by p processors prone to crashes. We assume that the distributed system is synchronous with processors communicating by message passing. Crashes are determined by a fully adaptive adversary that is restricted only by an upper bound f on the number of crashes. The complexity of algorithms is measured by work and communication, where work is defined as the number of available-processor steps, and communication as the number of point-to-point messages. We develop a randomized algorithm with W = O (t + p ṡ frac(log^{2} p, log log p)) expected work and O ((frac(p, p - f))^{3.4} W) expected communication, for an arbitrary number f < p of crashes.

Original language | English (US) |
---|---|

Pages (from-to) | 651-665 |

Number of pages | 15 |

Journal | Journal of Discrete Algorithms |

Volume | 6 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2008 |

Externally published | Yes |

### Fingerprint

### Keywords

- Crash failure
- Distributed algorithm
- Message passing
- Ramanujan graphs
- Randomization
- Scheduling tasks

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

### Cite this

*Journal of Discrete Algorithms*,

*6*(4), 651-665. https://doi.org/10.1016/j.jda.2008.03.001

**A robust randomized algorithm to perform independent tasks.** / Chlebus, Bogdan S.; Ga̧sieniec, Leszek; Kowalski, Dariusz R.; Shvartsman, Alex A.

Research output: Contribution to journal › Article

*Journal of Discrete Algorithms*, vol. 6, no. 4, pp. 651-665. https://doi.org/10.1016/j.jda.2008.03.001

}

TY - JOUR

T1 - A robust randomized algorithm to perform independent tasks

AU - Chlebus, Bogdan S.

AU - Ga̧sieniec, Leszek

AU - Kowalski, Dariusz R.

AU - Shvartsman, Alex A.

PY - 2008/12/1

Y1 - 2008/12/1

N2 - The Do-All problem is about scheduling t similar and independent tasks to be performed by p processors prone to crashes. We assume that the distributed system is synchronous with processors communicating by message passing. Crashes are determined by a fully adaptive adversary that is restricted only by an upper bound f on the number of crashes. The complexity of algorithms is measured by work and communication, where work is defined as the number of available-processor steps, and communication as the number of point-to-point messages. We develop a randomized algorithm with W = O (t + p ṡ frac(log2 p, log log p)) expected work and O ((frac(p, p - f))3.4 W) expected communication, for an arbitrary number f < p of crashes.

AB - The Do-All problem is about scheduling t similar and independent tasks to be performed by p processors prone to crashes. We assume that the distributed system is synchronous with processors communicating by message passing. Crashes are determined by a fully adaptive adversary that is restricted only by an upper bound f on the number of crashes. The complexity of algorithms is measured by work and communication, where work is defined as the number of available-processor steps, and communication as the number of point-to-point messages. We develop a randomized algorithm with W = O (t + p ṡ frac(log2 p, log log p)) expected work and O ((frac(p, p - f))3.4 W) expected communication, for an arbitrary number f < p of crashes.

KW - Crash failure

KW - Distributed algorithm

KW - Message passing

KW - Ramanujan graphs

KW - Randomization

KW - Scheduling tasks

UR - http://www.scopus.com/inward/record.url?scp=54449084777&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=54449084777&partnerID=8YFLogxK

U2 - 10.1016/j.jda.2008.03.001

DO - 10.1016/j.jda.2008.03.001

M3 - Article

AN - SCOPUS:54449084777

VL - 6

SP - 651

EP - 665

JO - Journal of Discrete Algorithms

JF - Journal of Discrete Algorithms

SN - 1570-8667

IS - 4

ER -